This invention relates generally to an apparatus for holding a workpiece. More particularly, this invention relates to a device for holding a rotatable workpiece during metalworking operations such as centerless grinding.
Grinding is one of the most effective machining methods to finish a workpiece for good dimensional accuracy and surface quality. Among the large family of grinding processes, centerless grinding is widely used to machine circular workpieces, such as the bearing rings, shafts, and rollers. The merits of the centerless grinding process include efficiency in loading and unloading workpieces and maintenance of desired geometric accuracy. Since centerless grinding is effective in terms of cost and precision, it has been widely used in manufacturing industries for many decades, especially in the anti-friction bearing industry.
Anti-friction bearings are among the most important mechanical elements used in modern industry. The application of bearings is so widespread that one may find them in almost every device; ranging from military weapons to medical equipment, machine tools, aerospace devices, and even children's toys. The widespread use of bearings has made bearing manufacturing one of the most important industries in the world.
One particular centerless grinding process, shoe centerless grinding, has been used throughout the bearing industry for machining workpieces such as bearing components. In this grinding process, a workpiece is driven by a magnetic drivehead, supported by a front and rear shoes, and machined by a grinding wheel, as illustrated in FIG. 1. The magnetic drivehead rotates at a prescribed rotational speed and drives the workpiece to rotate at a certain speed through the planar frictional contact between the drivehead and the workpiece. The magnetic intensity determines the normal force of the contact surfaces while an offset identifies the relative sliding velocity between the workpiece and the drivehead. Two shoes are used to support and locate the workpiece. The grinding wheel moves towards the workpiece to remove material from the workpiece and the circularity of the workpiece is uniquely determined by three contact points with the workpiece, the two shoes and the grinding wheel. A typical shoe centerless grinding is characterized by setup parameters such as two setup angles .alpha. and .beta., and the offset .delta. of the workpiece center with respect to the drivehead center; and by process parameters, such as drivehead magnetic intensity, the rotational speeds of the drivehead, workpiece and grinding wheel and the infeed rate of the grinding wheel.
Shoe centerless grinding also functions to attenuate the existing irregularities on the workpiece surface thereby increasing surface quality and dimensional accuracy. Since the workpiece is located and supported by two shoes, any variation in workpiece diameter can cause the workpiece center to move. The nature of the floating center of the workpiece distinguishes this process from center type grinding processes.
Out-of-roundness error of the workpiece has been a major concern in applying centerless grinding. The error usually results from the variation of the offset .delta. which is caused by two sources: workpiece dimensional change due to material removal and workpiece surface irregularities. When a surface irregularity is in contact with a support shoe, it forces the workpiece center to move away from the shoe surface by an amount equal to the height of the irregularity, thus causing a variation in the center offset .delta.. The variation in center offset will change the desired interacting position between the grinding wheel and the workpiece and therefore add a new irregularity to the workpiece surface. Geometrically and dynamically, when the irregularity passes over a support shoe, an undesirable perturbation is generated to the workpiece. If the amplitude of the perturbation is increased in the subsequent processes, the grinding system is considered to be geometrically and dynamically unstable, otherwise, it is considered to be stable. A stable grinding system is always preferred for achieving a workpiece with a good roundness and surface finish. However, a grinding system may become unstable due to the geometric, dynamic and workholding instability problems.
Geometric instability is mainly caused by the geometric setup of the grinding system. Workholding instability is induced by rotational variations of the workpiece, bounce of the workpiece from a support shoe, or the workpiece rotational speed matching that of the grinding wheel. Dynamic instability results from self-excited vibrations of the system. The workpiece perturbation induced by the grinding system may serve as a cause to initiate a self-excited vibration.
The above three instability problems have been recognized as critical problems to improvement of workpiece roundness in shoe centerless grinding processes for over a half century. However, these problems have not yet been satisfactorily solved.
In the shoe centerless grinding process, the magnetic drivehead provides a torque to the workpiece through offsetting the workpiece center with respect to the drivehead. The torque may be decomposed into a spin torque and a global torque. The global torque tends to drive the workpiece to rotate around the rotational center of the drivehead. However, the global torque cannot drive the workpiece to rotate around the rotational center of the drivehead because such a rotational motion would be stopped by the shoes, causing the workpiece to slip against the drivehead, and thus generating a driving force through friction that attempts to drive the workpiece to revolve about the drivehead. A spin torque is a driving torque that drives the workpiece to rotate around its own center through friction. Therefore, the workpiece is subjected to the driving force and the driving torque. Due to the nature of its constraints, the workpiece has three degrees of freedom and can only be allowed to have planar movement. To achieve workholding stability, two constraints are required to eliminate the two translational degrees of freedom; and the spin torque must be balanced to stabilize workpiece rotation. All the constraints to the workpiece, whether translational or rotational, can be varied in strength by varying the process parameters. Of these process parameters, the rotational speed of the drivehead, the magnetic intensity of the drivehead and the offset play important roles in workholding through which, the driving force and the driving torque regulate the workpiece movement. The relative motion of the workpiece with respect to the drivehead is a kinematic behavior of the workholding mechanisms. In order to obtain a stable workholding, the relative movement of the workpiece against the drivehead must be analyzed, the driving force and driving torque must be derived in terms of the process parameters, and workholding stability conditions need to be established.
In center-type grinding where a workpiece is securely held by workpiece centers, there is no workholding stability problem. However, in shoe centerless grinding, the workpiece is maintained in its nested position by the resulting system of forces provided by the shoes, drivehead, and grinding wheel. If the workpiece is maintained under a stable equilibrium condition, it is considered to be a case of stable workholding, otherwise, the following unstable workholding cases may occur.
a. The workpiece stops rotating but remains supported by the shoes; PA1 b. The workpiece loses contact with one or both shoes; PA1 c. The grinding force becomes the controlling force in the workpiece rotation, which tends to drive the workpiece to rotate at the same peripheral speed as the grinding wheel; PA1 d. The workpiece vibrates too violently to rotate under a normal grinding condition.
There have been no publicized reports dealing with the workholding stability and workholding mechanism in terms of grinding system kinematics and mechanics, although both of the issues are important and fundamental. In essence, the nature of workholding is determined by the driving capability and the constraining capability of a shoe centerless grinding system. The driving capability is featured by a driving force and a driving torque applied by the drivehead which is related to the rotational speed and magnetic intensity of the drivehead, the friction coefficient, the contact area and offset of the workpiece with respect to the drivehead. The constraining capability is evaluated by the reacting forces at two shoes and the grinding wheel which are determined by the shoe setup angles, the grinding conditions, and the friction coefficients between the workpiece and the shoes. An unstable workholding can result when the driving capability provided by a drivehead to a workpiece is saturated or the constraining capability of the centerless grinding process is not properly selected.